Document Type : Research Paper
Authors
1 Dept. MEES, Campus Brussels, KU Leuven, Warmoesberg 26, Brussels, Belgium.
2 DECE, Universidad de las Fuerzas Armadas, Sangolqui, Ecuador.
Abstract
Considering slowly varying functions (SVF), %Seneta (2019) Seneta in 2019 conjectured the following implication, for $\alpha\geq1$,
$$
\int_0^x y^{\alpha-1}(1-F(y))dy\textrm{\ is SVF}\ \Rightarrow\ \int_{0}^x y^{\alpha}dF(y)\textrm{\ is SVF, as $x\to\infty$,}
$$
where $F(x)$ is a cumulative distribution function on $[0,\infty)$. By applying the Williamson transform, an extension of this conjecture is proved. Complementary results related to this transform and particular cases of this extended conjecture are discussed.
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